{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Test1 Fall 2011

# Test1 Fall 2011 - ENEE 222 Signals and Systems Fall 2011...

This preview shows pages 1–2. Sign up to view the full content.

1 ENEE 222 Signals and Systems Fall 2011 –Test 1 – 2011 - 09 - 28 - Solutions All problems count the same 25 points Problem 1: (a 12.5 points) Given the matrix [ ] , find vectors v,w so that v T Aw= f. (b 12.5 points) How many floating point operations does it take to compute A 2 ? Solution: (a) Choose [ ] , in the product Aw this picks off the last column of A. Choose [ ] , in the product v T Aw this picks off the second element of Aw , which is f. (b) To obtain the 11 element of A 2 we multiply the first column of A by the first row of A and sum the products. This requires 3 multiplications and 2 additions. Repeating this to compute each of the 9 elements in A 2 we need 27 multiplies and 18 adds, a total of 45 floating point operations. Problem 2: Let G be an m 2 matrix and let u,v be defined by [ ] [ ] . (a 5 points) What are the dimensions of u,v ? (b 20 points) Express [ ] in terms of u and v. Solution: (a) The vectors are both m 1. (b) Let g 1 and g 2 be the columns of the matrix G, then the first expression gives - g 1 + g 2 = u and the second gives 2 g 1 + g 2

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 2

Test1 Fall 2011 - ENEE 222 Signals and Systems Fall 2011...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online